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Solving dual integral equations on Lebesgue spaces

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Ciaurri Ó., Guadalupe J. J., Pérez M., Varona J. L.

Studia Mathematica

2000

tom 142

nr 3

253-267

We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh's type. We reformulate these equations giving a better description in terms of continuous operators on $L^p$ spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series $∑_{n=0}^{∞} c_n J_{μ+2n+1}$ which converges in the $L^p$-norm and almost everywhere, where $J_ν$ denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution.

Ograniczanie wyników

1 Studia Mathematica

1 Ciaurri Ó.

1 Guadalupe J. J.

1 Pérez M.

1 Varona J. L.

1 2000

Wyniki wyszukiwania

Solving dual integral equations on Lebesgue spaces